Abstract. In this paper, we show how augmented Lagrangian alternating direction method (ADM) can be used to solve both the classical and ptychographic phase retrieval problems. We point out the connection between ADM and projection algorithms such as the hybrid input-output (HIO) algorithm, and compare its performance against standard algorithms for phase retrieval on a number of test images. Our computational experiments show that ADM appears to be less sensitive to the choice of relaxation parameters, and it usually outperforms the existing techniques for both the classical and ptychographic phase retrieval problems.

Ptychography is a popular technique to achieve diffraction limited resolution images of a two or three dimensional sample using high frame rate detectors. We introduce a relaxation of common projection algorithms to account for instabilities given by intensity and background fluctuations, position errors, or poor calibration using multiplexing illumination. This relaxation introduces an additional phasing optimization at every step that enhances the convergence rate of common projection algorithms. Numerical tests exhibit the exact recovery of the object and the noise when there is high redundancy in the data.